Question: Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{n^2 - 7n - 8}{n^2 - 8n}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 - 7n - 8}{n^2 - 8n} = \dfrac{(n + 1)(n - 8)}{(n)(n - 8)} $ Notice that the term $(n - 8)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n - 8)$ gives: $p = \dfrac{n + 1}{n}$ Since we divided by $(n - 8)$, $n \neq 8$. $p = \dfrac{n + 1}{n}; \space n \neq 8$